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• 4. Consider the additive group (,+).【題組】(a) What is the order of 6? Why?
• 8.Let with . Prove that if and , then .
• 三、選填題 14. 在坐標平面上，若圓 Γ 完全落在四個不等式：x−y  ≤ 4、x−y≥−2、x+y ≤18、x+y≥−24所圍成的矩形區域內，則 Γ 最大可能面積為______π 。（化成最簡分數
• 【題組】3.2 Please verify your answer by using Laplace transformation.
• 4. Please find the Fourier series of the function f(x) = cos3 2x+sin5 x.
• 7. The following series of branch outcomes occurs for a single branch in a program. Tmeans the branc
• 8.A computer whose processes have 1024 pages in their address spaces keeps its pagetables in memory.
• 1. 2018年全球最安全國家台灣排名為多少？　(A)34　(B)35　(C)36　(D)37　。
• Part B.Solving the following problems(50%)(每一大題10分,請務必寫出計算過程)(11) (10pt) Find the rank of A:
• 【題組】(b) Find all generators of the group.
• 5. Let matrix 【題組】5.1 Please find the eigenvalues and the corresponding eigenvector of the matrix A.
• 【題組】8.2 How long does each refresh command occupy the DRAM banks (in ns) such that across all theban
• 【題組】8.3 What data bus utilization, across all memory channels, is directly caused by DRAM refreshes?
• 【題組】8.4 How many refreshes are performed by the memory controllers during the 1.024 second period in
• 51. 將民眾力量納入國防力量，已經是全球的趨勢。例如國情威脅與我國相近的瑞士、以色列及新加坡，都是將國家安全與全民國防理念相結合，形成強大防衛動員力量。(A)O(B)X
• 5. Consider the multiplicative group ().【題組】(a) What is the order of the group? Why?
• 15. 設平面向量和互相垂直，且。若的長度為 6，則的長度為______。（化成最簡根式）
• (b) Buler's Theorem. For each n Ezt,n ＞ 1, and each a EZ, prove that if gcd(a,n) = 1,then (a中(n
• 【題組】5.2 Find matrix P that makes matrix A diagonal.
• 【題組】(b) Find the inverse of 25.
• 6. Let (ZxZ,⊕) be the group with (a, b)⊕(c, d) = (atc+2, 6+d-2) for any (a, b), (c, d) ∈ ZxZ wherea+
• 【題組】(b) What is the identity of the group?
• 【題組】(c) What is the inverse of (a, b)?
• 【題組】(d) [8%] Let (G, +) be an additive group and let h: ZxZ → G be a group homomorphism whereh(3, 2)
• 1. 動員準備機制則可區分為「物資動員」及「軍事動員」兩個子系統。(A)O(B)X